That's what also throws me off. The red Templars are still using their original Templar insignia, does that mean that they aren't rebel Templars and just unfortunates that ended up huffing red lyrium, meaning that there are now 3 types of Templars? (Red, loyal and rebel).You would think that the rebel Templars would want to ditch an insignia so heavily associated with the Chantry, right? Or perhaps that building is for the Divine loyal Templars/Cullen's faction and they kept the insignia for nostalgia purposes, especially if the Divine really does snuff it.
It's possible that there are three types of templars, though I think that it's possible that they made all the loyal templars part of the Seekers, and unite the Seekers and templars that left the Chantry in the Templar Order, which is then split with the Red templars. This might be supported by the earlier ring concept art, if the red ring rapresent the RT. The templar ring would rapresent the new templars (both templars and Seekers) that left the Chantry and the Seekers ring would rapresent the loyal Seekers who would include the templars that remained with the Chantry.
I don't think that the rebel templars would want to ditch the insignia. Lambert was more against Justinia than the Chantry. The reason why the Red templars use the same insignia might be because Bioware didn't want to confuse people by showing a 'templar' group with a completely different insignia.
I think it's still possible that the templars in Therinfal aren't RT due to the fact that we don't have much info yet, but I don't think it's very likely. It'd be extremely confusing if all the templars' factions use the same sign without even a difference in the colour scheme.